Question

Linear function 1. On a graypoints are (1, 9) and (2, 12) and passing through (0,6) on y axis

Linear function 2
x y
0 2
5 42
Compare the two functions which one has the greatest rate of change

Answer 1

To determine which function has the greatest rate of change, we can calculate the slope of each function.

For Linear Function 1:
We know that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
Using the points (1, 9) and (2, 12), we can calculate the slope:
(12 - 9) / (2 - 1) = 3

So, the slope of Linear Function 1 is 3.

For Linear Function 2:
We can calculate the slope using the given points (0, 2) and (5, 42):
(42 - 2) / (5 - 0) = 8

So, the slope of Linear Function 2 is 8.

Comparing the two slopes, we can see that Linear Function 2 has the greatest rate of change, as it has a greater slope of 8 compared to the slope of Linear Function 1, which is 3.